Calculating total work using kinetic-work theorem

In summary, a boy and a girl initially at rest on a frozen pond push each other causing them to slide in opposite directions. The total work done by the children can be calculated by adding their kinetic energies, which are 1/2(mv^2) for the boy and mv^2 for the girl. However, this does not result in the correct answer of 3mv^2, which can be explained by using conservation of momentum and understanding that the girl's mass is actually 2m. It is important to use clear notation and understand concepts thoroughly when solving problems.
  • #1
tjw137
4
0
1. A boy of mass m and a girl of mass 2m are initially at rest at the center of a frozen pond. They push each other so that she slides to the left at speed v across the frictionless ice surface and he slides to the right as shown above. What is the total work done by the children.



2. KE=1/2(mv^2)



3. I was thinking of adding the kinetic energies together. For the girl, I was thinking mv^2 and 1/2 mv^2 for the boy. This would give me 3/2(mv^2), but the correct answer should be 3mv^2. I need help understanding this concept, and how you would arrive to this conclusion. Thanks!
 
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  • #2
You are given that the speed of the girl is v, so how her KE be mv^2?

But first things first. How can you figure out the speed of the boy?
 
  • #3
By conservation of momentum! Thanks for pointing me in the right direction.
 
  • #4
Doc Al said:
You are given that the speed of the girl is v, so how her KE be mv^2?
But you were correct about that! (Her mass is 2m, not m. :redface:)

tjw137 said:
By conservation of momentum!
Exactly!
 
  • #5
I had written her mass in terms of the boys mass. I was not clear on that in my initial post. Sorry about that. I should have used subscripts.
 

FAQ: Calculating total work using kinetic-work theorem

1. How is total work calculated using the kinetic-work theorem?

The kinetic-work theorem states that the total work done on an object is equal to the change in its kinetic energy. This means that the total work can be calculated by finding the difference between the final and initial kinetic energy of the object.

2. Can the kinetic-work theorem be used for all types of motion?

Yes, the kinetic-work theorem can be used for all types of motion, including linear, circular, and rotational motion. As long as there is a change in the object's kinetic energy, the theorem can be applied.

3. What is the formula for calculating total work using the kinetic-work theorem?

The formula is W = ΔK = Kf - Ki, where W is the total work, ΔK is the change in kinetic energy, Kf is the final kinetic energy, and Ki is the initial kinetic energy.

4. How is the kinetic energy of an object calculated?

The kinetic energy of an object is calculated using the formula K = 1/2mv2, where m is the mass of the object and v is its velocity.

5. Can the kinetic-work theorem be used to calculate the work done by non-conservative forces?

No, the kinetic-work theorem can only be used to calculate the work done by conservative forces. Non-conservative forces, such as friction, do not have a potential energy associated with them and therefore cannot be represented in the change in kinetic energy.

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